This paper proposes a design method of 2-D variable IIR digital filters with high frequency tuning accuracy. In the proposed method, a parallel complex allpass structure is used as the prototype structure of the 2-D variable digital filters in order to obtain low sensitivity characteristic. Because the proposed 2-D variable digital filter is composed of first-order complex allpass sections connected in parallel, the proposed variable digital filter possesses several advantages such as low sensitivity characteristic in the passband, simple stability monitoring and high parallelism. In order to improve the frequency tuning accuracy of the proposed variable digital filter, each first-order complex allpass section is substituted by a new first-order complex allpass section with low sensitivity characteristic. Moreover, the coefficient sensitivity analysis of a 2-D parallel complex allpass structure is presented. Numerical examples show that the proposed 2-D variable IIR digital filter has high tuning accuracy under the finite coefficient wordlength.

This paper proposes a design method of variable IIR digital filters based on balanced realizations and minimum round-off noise realizations of digital filters. Highly accurate variable digital filters are easily derived by the proposed method. The coefficient matrices of both realizations of second-order digital filters are obtained directly from prototype realizations. The filter coefficients of variable digital filters can be obtained by frequency transformations to the realizations. The filter coefficients are presented as truncated Taylor series for the purpose of reducing a number of calculations to tune the coefficients. However the proposed filters have highly accurate variable characteristics against the coefficient truncation since balanced realizations and minimum round-off noise realizations have very low coefficient sensitivities, which are invariant under the frequency transformations. Moreover, the dynamic ranges of the proposed filters are almost constant against the frequency transformations. Numerical examples show the effectiveness of the variable digital filters designed by the proposed method.

It is often desired to change the cutoff frequencies of digital filters in some applications like digital electronic instruments. This paper proposes a design of variable lowpass digital filters with wider ranges of cutoff frequencies than conventional designs. Wave digital filters are used for the prototypes of variable filters. The proposed design is based on the frequency scaling in the s-domain, while the conventional ones are based on the z-domain lowpass-to-lowpass transformations. The first-order approximation by the Taylor series expansion is used to make multiplier coefficients in a wave digital filters obtained from a frequency-scaled LC filter become linear functions of the scaling parameter, which is similar to the conventional design. Furthermore this paper discusses the reduction of the approximation error. The curvature is introduced as the figure of the quality of the first-order approximation. The use of the second-order approximation to large-curvature multiplier coefficients instead of the first-order one is proposed.